A multi-timescale synaptic weight based on ferroelectric hafnium zirconium oxide

Brain-inspired computing emerged as a forefront technology to harness the growing amount of data generated in an increasingly connected society. The complex dynamics involving short- and long-term memory are key to the undisputed performance of biological neural networks. Here, we report on sub-µm-sized artificial synaptic weights exploiting a combination of a ferroelectric space charge effect and oxidation state modulation in the oxide channel of a ferroelectric field effect transistor. They lead to a quasi-continuous resistance tuning of the synapse by a factor of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$60$$\end{document}60 and a fine-grained weight update of more than \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$200$$\end{document}200 resistance values. We leverage a fast, saturating ferroelectric effect and a slow, ionic drift and diffusion process to engineer a multi-timescale artificial synapse. Our device demonstrates an endurance of more than \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${10}^{10}$$\end{document}1010 cycles, a ferroelectric retention of more than \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10$$\end{document}10 years, and various types of volatility behavior on distinct timescales, making it well suited for neuromorphic and cognitive computing.


Supplementary Note 2. Structural analysis
Grazing-Incidence X-Ray Diffraction (GIXRD) scan, taken after the crystallization of HZO and the extra WOx oxidation in a Rapid Thermal Annealer (RTA), is shown in Supplementary Figure 3

(a)
and confirms the ferroelectric orthorhombic phase of HZO. No monoclinic phase is observed, confirming the effectiveness of our Back-End-Of-Line (BEOL) compatible crystallization [1]. Further, the analysis indicates that the WOx stayed amorphous during the RTA oxidation step as the characteristic peaks are missing. For comparison, a GIXRD scan of a crystallized WOx (ICSD86144) [2] is shown in Supplementary Figure 3 (a). Bright-Field Scanning Transmission Electron Microscopy (BF-STEM) analysis displays the expected layer thicknesses and an amorphous WOx (Supplementary Figure 3 (b)). The rough topography of the W gate, originating from its columnar growth (Supplementary Figure 3 (d)), results in a projection effect (overlapping of measured elements) at layer boundaries as seen in the Energy-Dispersive X-ray Spectroscopy (EDS) line profile in Figure 1(b). Although the projection effect creates some uncertainty in the interpretation of the EDS data, two observations can be made: First, at the HZO/TiN interface a TiON layer was formed, possibly during the HZO growth by Atomic Layer Deposition (ALD). Second, Al diffusion into the WOx is measured (more pronounced than the artificial mixing by the projection effect). This is interesting as Al is expected to promote the reduction of WOx [3]. (By reducing WO3 to WO3-x, oxygen vacancies not only donate delocalized electrons to the conduction band but also modify the band structure [4], [5] near the Fermi level. Somewhere between = 0.167 and = 0.2, the Fermi level moves up into the conduction band while the density of states in the valence band is reduced and a structural phase transition occurs (W20O58 to W18O49) [6]). Supplementary Figure 3 (c,d) show Scanning Electron Microscope (SEM) images taken in a Focused Ion Beam (FIB) system. The cross-sectional view shows the result of the Mechanical Chemical Polishing (CMP) step that was performed to remove the topography after M2. Clearly, the passivation has the same height as the W metal lines. Supplementary Figure 3 (e,f) show a cross-sectional BF-STEM image of a crystallized HZO grain and the corresponding fast Fourier transform.

Supplementary Note 3. Gate capacitance and resistance
Devices with a channel length and width from 300 to 2 µ were fabricated to capture the geometrical influence on the device performance. In our design the gate (G) fully overlaps with the source (S) and the (D). The channel length is defined as the distance between the S and D contacts. First, the gate capacitance was measured across 30 FeFETs of different sizes and normalized by the gate area: A typical butterfly shaped capacitance dependence on the gate voltage ( ! ) was observed with ! = 24 • µ "# at ! = 0 ( Supplementary Figure 4(a)). This is in good agreement with previous studies [7]. The gate resistance ( ! ) was measured on the same 30 FeFETs by applying a ! from 1 to 5 while grounding source and drain (Supplementary Figure 4(b)). At 1 the gate resistance is 740 • µ # , while at 5 V it decreases to 39 • µ # . Both values are high impedance and allow for low power writing. In addition, decreasing the device size reduces the power dissipation even more.

Supplementary Note 5. Time and channel length dependent dynamic range
The infulence of the write pulse width ( ' ) on the dynamic range (DR) was obtained by measuing potentiation and depression ( ' ± 6 ) on 120 FeFETs with a channel width $( of 600 and variyng channel length $( from 300 nm to 2 µm. Repeating the same measuremnt for a ' of 500 µ (Figure 1(b)) and 500 (Supplementary Figure 6 (a)) showed a clear dynamic range increase with increasing ' . Supplementary Figure 6(b) shows the factor by which the dynamic range increased by increasing tw as a function of the channel length. There is a small dependence on the channel length.
We can now define the total source-to-drain resistance as ) is the resistance of the WOx channel without the contact resistance (2Rc). Plotting the LRS and HRS as a function of the channel length (Supplementary Figure 7(a)) is similar to transmission line measurements (TLM) and allows to extract the contact resistance (2 $ ) at the y-intercept and the resistivity of the channel (ρ) from the slope of the linear regression. The extracted values for ' = 500 µ and ' = 500 are summarized in Supplementary Table 1. Multiple observations can be made: First, the $ modulation has a greater influence on the DR than the modulation. The same conclusion holds when comparing the DR by increasing ' : The effect is more pronounced for $ than for . and a channel length varying from 300 to 2 µ . Write pulses with an amplitude ( $ ) from −6 to 6 and width (t $ ) of 500 µ were applied. The boxes extend from the lower to upper quartile values of the data, with a line at the median. The whiskers extend from the box to show the range of the data. Flier points are those past the end of the whiskers. (b) Factor by which the dynamic range increased by going t $ = 500 µ (Figure 1(b)) to t $ = 500 as a function of channel length. Note that the outlier with a high dynamic range at the channel length 0.4 µ increases the slope. Figure 7(b) shows the LRS and HRS for ' = 500 µ and ' = 500 with 2 $ subtracted and scaled by the channel dimensions as a function of the channel length

Supplementary
). The fact that the linear regression has almost no slope shows that $( scales with the geometry of the channel and that there is very little dependence of the 6 #$ on the channel length. The dependence of the DR on the channel length must originate from the difference in the ratio of ; #$ and ; # for different channel lengths.  Figure 7(a).

Supplementary Note 6. Oxygen movement
The ferroelectric effect is field-dependent and the polarization is supposed to saturate as soon as all domains have switched. In a FeFET this should translate into a saturation of the channel resistance as soon as the entire ferroelectric layer has switched. Supplementary Figure 9 shows a non-saturating channel resistance when applying 90 identical pulses with ' = 6 and ' = 100 , indicating that there is a second effect like oxygen movement involved in the modulation. . Even after 100 pulses no clear saturation can be seen.

Supplementary Note 7. Temperature dependent conduction measurements
Temperature dependent current measurements of the channel were conducted for two reasons: on one hand to characterize the WOx channels conduction mechanism. On the other hand, to further prove that two different effects are contributing to the resistance modulation of the channel at different timescales. The experiment was conducted as follows. At each temperature, the device was first set to its HRS, then the channel current (IDS) was measured by applying an I-V sweep from )* = −200 to )* = 200 . Then the same was repeated for the LRS. After the I-V measurements were conducted, the temperature was increased. To stabilize the temperature, we waited 10 min before starting with the next I-V sweeps. The following equation describes the ohmic conduction: where )* is the current density, the electrical conductivity, µ the electron mobility, is the electronic charge, < the carrier concentration, ( < − F ) the energy difference between the conduction band and the Fermi level, the Boltzmann constant, the absolute temperature, VSD the source-drain voltage and $( the length of the channel. Supplementary Figure 8 shows temperature dependent current measurements of the channel. Supplementary Figure 8 ). This then allows to use Equation (1) to determine the < product, under the assumption that G is temperature independent [13]. The dynamic range became smaller with increasing temperature as shown in Supplementary Figure 8(c). This effect could be due to a phase transition from the orthorhombic ferroelectric phase of HZO to the tetragonal, antiferroelectric phase at elevated temperatures, as observed in ZrO2 [14] and Si:HfO2 [15]. The same experiment was repeated where the HRS was set by 90 pulses of ' = 100 and ' = 6 , representing a much longer timescale (Supplementary Figure 8(d)). As can be seen in Supplementary Figure 9, a complete saturation of the HRS was usually not reached. Again, the current can be fitted with a linear regression with = 1. The corresponding Arrhenius plot (Supplementary Figure 8(e)) is used to extract < − F and < . Since the HRS does not saturate, it is difficult to argue that at each temperature the same state is reached and hence also explains why the conduction in Supplementary Figure 8(e) does not linearly depend on 1/ . In other words, using the same pulses to set the HRS at different temperatures will result in a different oxidation state of the WOx for each temperature. The extracted parameters are summarized in Supplementary Table 2 where the values for the HRS should be treated with caution as explained above. Finally, Supplementary Figure 8(f) shows a dynamic range that increases with temperature, exactly what we expect if the resistance modulation is dominated by oxygen movement: the mobility of oxygen increases with temperature which leads to an enhanced oxidation and reduction of the channel. In summary, this experiment clearly shows the ohmic nature of our WOx channel at read voltages ( )* = ± 200 ) for both the LRS and HRS. Especially by looking at the dynamic range dependence on temperature we can further prove that two different mechanisms resistance at two different timescales modulate the channel resistance.